Determine how many solutions exist for the system of equations. ${x+y = 6}$ ${-x+y = 8}$
Answer: Convert both equations to slope-intercept form: ${x+y = 6}$ $x{-x} + y = 6{-x}$ $y = 6-x$ ${y = -x+6}$ ${-x+y = 8}$ $-x{+x} + y = 8{+x}$ $y = 8+x$ ${y = x+8}$ Just by looking at both equations in slope-intercept form, what can you determine? ${y = -x+6}$ ${y = x+8}$ The linear equations have different slopes. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ When two equations have different slopes, the lines will intersect once with one solution.